[en] Gaussian beams that include a set of phase functions having a purely quantum mechanical analog are examined; these are coherent states, correlated and discrete modes for quantum oscillators that model optical fibers. In propagating through free space these beams lose coherence and aberrations appear. The authors describe these aberrations and investigate such observables as the beam center, the beam width and the evolution of the correlation coefficient. This is done for systems described by optical models having a Hamiltonian that is an arbitrary function of the momentum expanded into a series and diverging in a certain region including the optical axis. The paraxial approximation is investigated in detail as a particular case of accounting for only the first term in the expansion